Observation and description of changes in the world around us are the first steps in finding and learning about patterns.
Investigation 3 Essential Question:
How can I visually explain situations where one thing changes based on another?
New Vocabulary
New Vocabulary
Definition
Income =
The amount of money you receive from doing labor, services, or selling goods.
Cost =
The price you have to pay (usually in money) to get a product or service.
Profit =
The profit is your income-cost.
Commutative =
In mathematics this is a property where changing the orders of the numbers doesn’t affect the end result.
Notes from Class
You can find the profit by doing income-cost=profit. So for example if 20 is the income and 15 is the cost, then the profit would be 5 because 20-15=5.
Commutative = addition and multiplication
Noncommutative = subtraction and division
Problem 3.3: Predicting Profit
Based on the result of their survey, the tour operators decided to charge $350 per person for the tour. Of course, not all of this money would be profit. To estimate their profit, they had to consider the expenses involved in running the tour. Sidney estimated these expenses and calculated the expected profit for various numbers of customers. She made the graph below to present her predictions to her partners. Since the profit depends on the number of tour customers, she put the number of customers on the x-axis.
|A| How much profit will be made if 10 customers go on the tour? 25 customers? 40 customers?
For 10 customers, the profit would be $150. For 25 customers, the profit would be $375. For 40 customers, the profit would be $600.
|B|How many customers are needed for the partners to earn a $200 profit? A $500 profit? A $600 profit?
To make a $200 profit, you would need 14 customers. To make a $500 profit, you need 34 customers. To make a $600 profit, you need 40 customers.
|C|How does the profit change as the number of customers increases? How is this pattern show in the graph?
The profit changes are $75 for 5 customers. This pattern is shown in the graph because in the graph the data is in a straight line going upward.
|D| If the tour operators reduced their expenses, but kept the price at $350, how would this change the graph?
If you reduce the expenses, but kept the price at $350, then the profit goes up. This would show in the graph because at the start of the graph the graph would be going up normally, but toward the end it would start going up by less so it would start looking like a slope.
Problem 3.3 Follow Up
In the profit graph, points at the intersection of two grid lines, such as (20, 300) and (40,600),are easy to read. Use the “easy to read” points to figure out what the profit would be if only 1 customer went on the tour. How about 2 customers? 3 customers? 100 customers? Describe, in words, the estimated profit for any number of customers
For one customer the profit would be $15. For two customers the profit would be $30. For the 3 customers the profit would be $45. For 100 customers the profit would be $1,500. I found out the profit of 1 customer by first taking points at the intersections of two lines such as (20, 300). Then I have to divide 20 until I get 1 so what I did was I took out 1 zero from 20/300 and got 2/30. Then I divided 2/30 by 2 so I got 1/15. Now that I know that I customer=$15 profit, I can find the profit of how many customers by multiplying the number of customers by 15.
September 18, 2010
Math 7B
Variables and Patterns
Big Idea:
Observation and description of changes in the world around us are
the first steps in finding and learning about patterns.
Investigation 3 Essential Question:
How can I visually explain situations where one thing changes based on another?
New Vocabulary
Notes from Class
You can find the profit by doing income-cost=profit. So for example if 20 is the income and 15 is the cost, then the profit would be 5 because 20-15=5.
Commutative = addition and multiplication
Noncommutative = subtraction and division
Problem 3.3: Predicting Profit
Based on the result of their survey, the tour operators decided to charge $350 per person for the tour. Of course, not all of this money would be profit. To estimate their profit, they had to consider the expenses involved in running the tour. Sidney estimated these expenses and calculated the expected profit for various numbers of customers. She made the graph below to present her predictions to her partners. Since the profit depends on the number of tour customers, she put the number of customers on the x-axis.
|A| How much profit will be made if 10 customers go on the tour? 25 customers? 40 customers?
For 10 customers, the profit would be $150. For 25 customers, the profit would be $375. For 40 customers, the profit would be $600.
|B| How many customers are needed for the partners to earn a $200 profit? A $500 profit? A $600 profit?
To make a $200 profit, you would need 14 customers. To make a $500 profit, you need 34 customers. To make a $600 profit, you need 40 customers.
|C| How does the profit change as the number of customers increases? How is this pattern show in the graph?
The profit changes are $75 for 5 customers. This pattern is shown in the graph because in the graph the data is in a straight line going upward.
|D| If the tour operators reduced their expenses, but kept the price at $350, how would this change the graph?
If you reduce the expenses, but kept the price at $350, then the profit goes up. This would show in the graph because at the start of the graph the graph would be going up normally, but toward the end it would start going up by less so it would start looking like a slope.
Problem 3.3 Follow Up
In the profit graph, points at the intersection of two grid lines, such as (20, 300) and (40,600),are easy to read. Use the “easy to read” points to figure out what the profit would be if only 1 customer went on the tour. How about 2 customers? 3 customers? 100 customers? Describe, in words, the estimated profit for any number of customers
For one customer the profit would be $15. For two customers the profit would be $30. For the 3 customers the profit would be $45. For 100 customers the profit would be $1,500. I found out the profit of 1 customer by first taking points at the intersections of two lines such as (20, 300). Then I have to divide 20 until I get 1 so what I did was I took out 1 zero from 20/300 and got 2/30. Then I divided 2/30 by 2 so I got 1/15. Now that I know that I customer=$15 profit, I can find the profit of how many customers by multiplying the number of customers by 15.